Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Quantum states and phases in driven open quantum systems with cold atoms


An open quantum system, the time evolution of which is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the coupling between the system and the reservoir. This provides a route towards preparing many-body states and non-equilibrium quantum phases by quantum-reservoir engineering. Here, we discuss the example of a driven dissipative Bose–Einstein condensate of bosons and of paired fermions, where atoms in an optical lattice are coupled to a bath of Bogoliubov excitations and the atomic current represents local dissipation. In the absence of interactions, the lattice gas is driven into a pure state with long-range order. Weak interactions lead to a weakly mixed state, which in three dimensions can be understood as a depletion of the condensate, and in one and two dimensions exhibits properties reminiscent of a Luttinger liquid or a Kosterlitz–Thouless critical phase at finite temperature, with the role of the ‘finite temperature’ taken by the interactions.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Driven dissipative condensate.
Figure 2: Appearance of quasi-long-range order during the time evolution.

Similar content being viewed by others


  1. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).

    Google Scholar 

  2. Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004).

    Google Scholar 

  3. Kinoshita, T., Wenger, T. R. & Weiss, D. S. Observation of a one-dimensional Tonks–Girardeau gas. Science 305, 1125–1128 (2004).

    Google Scholar 

  4. Paredes, B. et al. Tonks–Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004).

    Google Scholar 

  5. Fölling, S. et al. Direct observation of second-order atom tunneling. Nature 448, 1029–1032 (2007).

    Google Scholar 

  6. Zwierlein, M. W., Schirotzek, A., Schunck, C. H. & Ketterle, W. Fermionic superfluidity with imbalanced spin populations and the quantum phase transition to the normal state. Science 311, 492–496 (2006).

    Google Scholar 

  7. Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998).

    Google Scholar 

  8. Petrov, D. S., Shlyapnikov, G. V. & Walraven, J. T. M. Regimes of quantum degeneracy in trapped 1D gases. Phys. Rev. Lett. 85, 3745–3749 (2000).

    Google Scholar 

  9. Góral, K., Santos, L. & Lewenstein, M. Quantum phases of dipolar bosons in optical lattices. Phys. Rev. Lett. 88, 170406 (2002).

    Google Scholar 

  10. Rezayi, E. H., Read, N. & Cooper, N. R. Incompressible liquid state of rapidly rotating bosons at filling factor 3/2. Phys. Rev. Lett. 95, 160404 (2005).

    Google Scholar 

  11. Büchler, H. P., Hermele, M., Huber, S. D., Fisher, M. P. A. & Zoller, P. Atomic quantum simulation for lattice gauge theories and ring exchange models. Phys. Rev. Lett. 95, 040402 (2005).

    Google Scholar 

  12. Rey, A. M., Gritsev, V., Bloch, I., Demler, E. & Lukin, M. D. Preparation and detection of magnetic quantum phases in optical superlattices. Phys. Rev. Lett. 99, 140601 (2007).

    Google Scholar 

  13. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

    Google Scholar 

  14. Gardiner, C. W. & Zoller, P. Quantum Noise (Springer, Heidelberg, 2000).

    Google Scholar 

  15. Baumgartner, B., Narnhofer, H. & Thirring, W. Analysis of quantum semigroups with GKS Lindblad generators: I. Simple generators. J. Phys. A 41, 065201–065220 (2008).

    Google Scholar 

  16. Baumgartner, B. & Narnhofer, H. Analysis of quantum semigroups with GKS Lindblad generators: II. General. Preprint at <> (2008).

  17. Kraus, B. et al. Preparation of entangled states by quantum Markov processes. Phys. Rev. A (in the press); preprint at <> (2008).

  18. Aspect, A., Arimondo, E., Kaiser, R, Vansteenkiste, N. & Cohen-Tannoudji, C. Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping. Phys. Rev. Lett. 61, 826–829 (1988).

    Google Scholar 

  19. Kasevich, M. & Chu, S. Laser cooling below a photon recoil with three-level atoms. Phys. Rev. Lett. 69, 1741–1744 (1992).

    Google Scholar 

  20. Gottesman, D. Stabilizer Codes and Quantum Error Correction. Thesis, California Inst. Technol. (1997).

  21. Vidal, G. Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91, 147902 (2003).

    Google Scholar 

  22. Verstraete, F., Wolf, M., Perez-Garcia, D. & Cirac, J. I. Projected entangled states: Properties and applications. Int. J. Mod. Phys. B 20, 5142–5153 (2006).

    Google Scholar 

  23. Verstraete, F., Wolf, M. M. & Cirac, J. I. Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation. Preprint at <> (2008).

  24. Griessner, A., Daley, A. J., Clark, S. R., Jaksch, D. & Zoller, P. Dark-state cooling of atoms by superfluid immersion. Phys. Rev. Lett. 97, 220403 (2006).

    Google Scholar 

  25. Moskalenko, S. A. & Snoke, D. W. Bose–Einstein Condensation of Excitons and Biexcitons (Cambridge Univ. Press, Cambridge, 2000).

    Google Scholar 

  26. Yang, C. N. η pairing and off-diagonal long-range order in a Hubbard model. Phys. Rev. Lett. 63, 2144–2147 (1989).

    Google Scholar 

  27. Demler, E., Hanke, W. & Zhang, S.-C. SO(5) theory of antiferromagnetism and superconductivity. Rev. Mod. Phys. 76, 909–974 (2004).

    Google Scholar 

  28. Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989).

    Google Scholar 

  29. Schön, G. & Zaikin, A. D. Quantum coherent effects, phase transitions, and the dissipative dynamics of ultra small tunnel junctions. Phys. Rep. 198, 237–413 (1990).

    Google Scholar 

  30. Haldane, F. D. M. Effective harmonic-fluid approach to low energy properties of one-dimensional quantum fluids. Phys. Rev. Lett. 47, 1840–1843 (1981).

    Google Scholar 

  31. Bistritzer, R. & Altman, E. Intrinsic dephasing in one dimensional ultracold atom interferometers. Proc. Natl Acad. Sci. USA 104, 9955–9959 (2007).

    Google Scholar 

  32. Burkov, A. A., Lukin, M. D. & Demler, E. Decoherence dynamics in low-dimensional cold atom interferometers. Phys. Rev. Lett. 98, 200404 (2007).

    Google Scholar 

  33. Donner, T. et al. Critical behavior of a trapped interacting Bose gas. Science 315, 1556–1558 (2007).

    Google Scholar 

  34. Hofferberth, S., Lesanovsky, I., Fischer, B., Schumm, T. & Schmiedmayer, J. Non-equilibrium decoherence dynamics in one-dimensional Bose gases. Nature 449, 324–327 (2007).

    Google Scholar 

Download references


We thank E. Altman, E. Demler and M. Lukin for discussions. Work at the University of Innsbruck is supported by the Austrian Science Foundation and EU grants SCALA and OLAQI.

Author information

Authors and Affiliations


Corresponding author

Correspondence to S. Diehl.

Supplementary information

Supplementary Information

Supplementary Information (PDF 73 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Diehl, S., Micheli, A., Kantian, A. et al. Quantum states and phases in driven open quantum systems with cold atoms. Nature Phys 4, 878–883 (2008).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing